Persistence is not Independence: A structural Credibility Protocol for Distribution based Recovery in VARLiNGAM

VAR-LiNGAM recovers a contemporaneous structure from reduced-form innovations under mutual independence of the underlying structural shocks. Recovery itself and bootstrap stability of the recovered edges are natural post-estimation outputs, but neither directly assesses the identifying independence assumption. We organize post-recovery validation as an ordered, non-compensatory protocol with four layers (reduced-form admissibility, distributional informativeness, independence support and edge persistence) and establish, by a constructive population result, a Monte Carlo experiment under known ground truth and a firm-level Compustat application, that the last two layers are non-nested: an edge can persist under resampling while the recovered shocks remain dependent, and independence can be supported while the leading recovered edge fails to persist. Independence support is classified operationally by a block-permutation dHSIC diagnostic on the recovered shocks, with mutual information as a continuous measure of residual dependence and tail co-exceedance as a complementary extreme-dependence diagnostic. Empirically, the conjunction of no detected independence violation and a reportable persistent leading edge occurs only in a small subset.